**Title:** Differences and the primes

**Speaker:** Tom Sanders

**Speaker Info:** IAS

**Brief Description:**

**Special Note**:

**Abstract:**

A common problem in arithmetic combinatorics is to ask how large a subset A of the integers {1,...,N} may be and still have the difference set A-A:={a-a':a,a' \in A} avoid some given set S. Examples of such sets S are the sets of squares, cubes or shifted primes, that is {p-1:p is prime}. Very often ergodic theory can give qualitative results indicating that A cannot be a positive proportion of {1,...,N}, however, for these simple problems there are also considerably stronger quantitative tools available. In this talk we shall focus on how to achieve good quantitative information on how large A may be when is avoids the set of shifted primes.Joint work with I Z Ruzsa

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